Hunting For Snipe

Over at Worthwhile Canadian Initiative, Nick Rowe continues to wage his crusade. (See also here, here, here, here, here, here, here, here, here, here).

It is tough going for monetarists. Once you add financial institutions to your model, it turns out that quantitative easing hardly affects the quantity of money held by the non-financial sector at all, but is (effectively) an asset swap between the government and the financial sector, affecting the non-financial sector only via the channel of interest rates. Moreover, risk-free interest rates are low, households prefer to store marginal increments in wealth in the form of bonds rather than deposits, and central banks have given up on targeting monetary aggregates. The history of trying to manage the economy by managing the quantity of money has been a dismal failure predicated on not understanding how the financial institutions actually operate, or even what their primary mission is. It seems popular to view central banks as managers of aggregate demand, and ignore the trillions of dollars in income support payments flowing out of Treasury each year.  However the first and foremost job of the central bank is to ensure a flexible money supply so that the its core constituency — banks — are able to convert illiquid collateral into money on demand.  Any additional responsibilities are secondary, and can never interfere with this core mission, which is to make false the assumptions of the old school monetarist model. By ensuring that certain types of collateral are liquid — i.e. can be converted into money or used to borrow money — in all circumstances, the money supply becomes demand determined and is no longer a choice variable. And it cannot be a choice variable if we are to have a sound financial sector. The marginal cost of reserves is a choice variable. Bank regulation is a choice variable, collateral requirements are a choice variable, but the quantity of money is a state variable that is determined endogenously by the response of the private sector to these policies.

So why the obsession on market clearing and excess demand for money? Because the real problems faced by the economy are assumed away, and all that is left is a comical search for which market isn’t clearing. The markets are clearing just fine, nevertheless they are clearing in a way that provides less output and employment.

Economic Activity is not well modeled by an auction process

In an auction actors freely bid according to their preferences on a fixed set of endowments. Think of an estate sale. The endowments come from elsewhere.

The belief that, with full market clearing,  real income is exogenously determined is responsible for our market fundamentalism.

You can only force production onto the Procrustean bed of an exchange process by assuming that production occurs in zero time. Only in that case can you model the firm hiring the worker and paying them with a portion of the worker’s output. The output must be available at the same instant that the worker is hired.

But capitalism is first and foremost about time — production requires non-zero time, and there is an ever greater lengthening of time from first input to final output. Microsoft spent years paying engineers to develop the next version of their office product. After those years of development, they then sold mass copies of this product, justifying the labor payments ex-post.  But during those years of development, the workers were paid prior to the production process being complete, and with their payments, they purchased other products that were also produced in previous periods by other firms.

The capitalist process is not a process of exchange, but of investment. You make outlays in the present period without realizing a return on those outlays in the same period. The return occurs in subsequent periods. Fundamental to the investment decision is an expectation of the future price for which you will sell your output in relation to the present price with which you pay inputs.

It impossible for the investor to hedge that price. Therefore if prices are expected to decline,  firms are less willing to pay to produce output today, because they are paying more, in real terms, today, for goods that will be available to be sold in the next period. The labor demand curve shifts to the left and output declines.  When consumption prices are expected to increase, the real labor demand curve shifts to the right.  When the ratio of capital goods prices to consumption goods prices is increasing, the labor demand curve shifts to the right, when this ratio is declining, the labor demand curve shifts to the left.

In no sense can you argue that output is exogenously determined — that the “endowments” are somehow independent of the expected time path of the price vectors. That is why you often hear of output gaps as “throwing output away” — they truly believe the output is there, even though no one is hired to produce it. What may be thrown away are opportunities, but not output.  The production process is not an auction of exogenously set endowments.

You don’t need to hunt for snipe — for which market isn’t clearing — the markets are clearing with lower real incomes.  An economy is not an estate-sale.

Now it is possible to concoct examples of economies in which real income is unchanged provided that all markets clear. For example, fruit ripening on a vine that requires no human input. Or backstrach economies in which production truly is instantaneous.

What these models  have in common is that they deny the fundamental essence of a capitalist economy — of the production process as a risky process that cannot be hedged and that requires immediate payment in exchange for the possibility of future revenue in subsequent periods  It is a leap-frog model in which, at any time, defection can cause real income to decline. Households pay to consume present goods with the income they receive from the production of goods that will be sold in the future. Such a model has equilibria in which output is below potential and yet all markets are clearing with perfectly flexible prices.

My view is that this, rather than the estate-sale model, is a more appropriate approach to understanding recessions and depressions. Things like downward nominal wage stickiness just aren’t important.  If prices and wages were perfectly flexible then things would be as bad as they are now, at least to a first order approximation.

Hunting For Snipe

12 thoughts on “Hunting For Snipe

  1. Wow! You have read a lot of my posts!

    OK. Assume that labour input today produces output for consumption 1 year from today (or 10 years, if you like). Assume the output and labour markets are clearing. So W(t)/[(1+i)P(t+1)] is the relevant relative price. Why is there a big drop in employment?

    Was it a change in consumption/leisure preferences (contagious laziness)?
    Was it a change in time-preference (people stop working because they are too impatient to wait a year)?
    Was it a change in technology (people stop planting vines because vines produce less fruit than before, so it doesn’t seem worth the effort)?

  2. Yes, I do read your posts — they are enjoyable and educational.

    OK, are you asking why prices are changing or what the effects of the price changes are? They are different questions.

    The effects of declining prices is easy: from the point of the view of the firm, the MRP of the worker needs to priced in terms of next period’s prices. But from the point of view of the worker, they are measuring their current wages in terms of current period consumption prices. So the labor demand curve shifts to the left as a result of (expected) lower future revenue on the part of the firm, and it shifts to the right as a result of expected higher future revenue for the firm. And there are similar shifts when the ratio of capital to consumption goods prices change, with a leftward labor demand shift when capital goods decline in price (relative to consumption goods), and a rightward shift when capital goods increase in price, etc.

    Now the question is why would prices change in the first place? A whole host of reasons. Self-fulfilling prophecies, an increase in savings demands, etc. Once you have these feedback loops, then the system is locally unstable, so you do not need a reason to explain why an unstable system changes with time. Take a look at the time path of GDP deflator for consumption versus investment goods. It looks like a sine wave and a cosine wave, with one going up and the other down and vice versa. Similarly, take a look at the net present value of household wealth as a function of time. Wildly unstable, so it makes sense that as household wealth is revalued up and down, the result is changing consumption demand, which results in changing prices (in a flexible price model).

  3. Aha! rsj! So this is where you hang out.

    Put Leisure at time t on one axis, and Consumption at time t+1 on the other. Draw an indifference curve and a PPF. If one is concave, and the other convex, there should be a single equilibrium where they are tangent to each other. The slope at that tangency should equal W(t)(1+i)/P(t+1). [I made a math slip in my above comment, as usual, but I think I’ve got it right this time.]

    Or, with W(t)(!+i)/P(t+1) on the vertical axis, and Labour on the horizontal, you can draw a labour supply and a labour demand curve. And they will cross only once if preferences are concave and technology convex (or whatever, since I always get muddled).

    You *could* get multiple equilibria, and hence self-fulfilling prophecies, with the right assumptions about technology and preferences. Like strongly increasing returns to scale, or something. But the labour supply curve just seems to be too inelastic for that to be plausible.

    With a unique equilibrium, you have a fairly standard RBC model. You need a shock to technology or preferences to get it to work. Increased impatience, for example, would cause a decline in output and employment, but also an increase in the real interest rate and real wages.

  4. Nick,

    There is no market in which you can set P(t+1). Leisure at time t can give you a labor supply curve at time t, which we assume constant (as preferences for leisure are not changing). But we do not have complete markets in which you can purchase (or sell) future consumption at t+1 in exchange for present leisure.

  5. But I agree that the two curves will cross only once.

    There is a utopian solution.

    But there is no market mechanism to arrive at such a solution if workers cannot sell their labor forward or purchase their consumption forward — the obstacle is not rigid prices, but missing markets. The real wage to the worker is the present wage divided by the present prices of goods that they would purchase with that wage. They cannot purchase in period t consumption in period t+1.

  6. RSJ: OK. This is more promising. So we have to replace P(t+1) with people’s *expectations* of P(t+1). And if those expectations are “wrong”, in some sense, the perfectly flexible wage/price equilibrium may be “wrong” too.

    Now it’s starting to sound a bit more like Lucas 1972, (or maybe Austrian BCT?).

    Next step: in what sense would expectations have to be “wrong” in order to get a business cycle? Lucas’ answer is that each agent has to get a wrong belief about his own price relative to the general price level. For example, index the P’s by firms, f. If each agent expects his own future relative price Pf(t+1)/P(t+1) will be low (so when we aggregate we get sum over f of Pf(t+1)/P(t+1) <1), then we get a recession.

    And what could cause all agents to make mistakes in the same direction? Lucas said a monetary shock, where agents are better informed about the prices of the goods they produce and sell than about the prices of the goods they buy. There's a monetary shock, but agents can't distinguish monetary from real relative shocks, so each one thinks the demand for his particular product has fallen, relative to other products, so responds by working less.

  7. No, this is the Island Model rotated by 90 degrees 🙂

    In the Island Model, Lucas assumes instant production, so inflation has no effect — the effect comes from believing it is an increase in real income. Lucas is assuming that there are different geographies — e.g. types of products, and relative differences at the same point in time affect production decisions on each island. A timely production model would convert the spatial distance into a temporal distance — there are different stages of production, and relative price differences at each stage affect production.

    The simplest possible such model is that it takes 1 period of labor input to produce a product. The labor input is paid in period t. The product is sold in period t+1, with any revenues in excess of previously paid labor being profits (delivered to capital). The two temporal inputs are labor and capital, whose payments are separated by time. As labor is paid today, labor demand is unaffected by inflation. Inflation causes the (nominal) capital return to increase. But say the nominal capital return demanded is
    set by the Central Bank, or via arbitrage with the central bank rate. Whenever the nominal capital return is higher than the bank rate, firms will continue hire more variable inputs today up until no arbitrage is possible.

    Here, perceived inflation has a direct effect whereas unexpected increases inflation has no effect — it is the opposite of the Island Model.

    When more output produced today (to be sold in the next period) there is more present income with which to buy previously produced output. As the quantity of output available to buy in each period is fixed by production decisions made in the previous period, this translates into higher present prices the prophecies are self-fulfilling in a flexible price model, which adds instability. A rigid price model would be more stable.

    But the prophecies are self-fulfilling only up to a point. At some level of inflation, the falling real wealth (e.g. nominal wealth divided by the price level, which is going up) will overcome the low real rates and cause households to want to consume less today, not more, in order to rebuild their savings. At that point, the prophecy stops becoming self-fulfilling. Then, you can get self-fulfilling prophecies in the downward direction.

    I don’t *think* what I’m describing is an RBC model.

  8. OK. First assume it’s a barter model. Workers produce grape juice. Capitalists (savers) give the workers wine in exchange for grape juice.

    If preferences and technology are well-behaved, there will be a unique equilibrium. What causes that equilibrium to shift? Some real shock to preferences, technology, or expectations of preferences or technology. That’s an RBC.

    Now add money. Introduce a central bank that sets a nominal interest rate. If the central bank sets a nominal interest rate such that the ex ante (perceived) real interest rate is below the equilibrium real interest rate in the barter model, there will be an increased demand for grape juice and labour. If you add sticky prices/wages and monopolistic competition, you then get a New Keynesian model and a boom. But if prices and wages are perfectly flexible, that excess demand causes P and W to instantly explode to infinity.

    The Lucas twist was to add a supply response, so output and employment increased in response to that increase in AD, and P and W did not go to infinity. If you don’t like the Lucas twist, and don’t like the NK twist, I don’t see how you can get a finite level of P and W, and a boom.

  9. OK. This is a good point. The reason why prices explode to infinity in your case — which is the same reason you cannot find a competitive equilibrium with increasing returns — is that production requires zero time.

    As soon as production requires non-zero time, then this prevents the infinity. You only get finite inflation.

    It is very similar to your (excellent) “non-function” characterization of perfect competition: If a firm sells a bit below the equilibrium price, demand for its product is infinite, and a bit a above, demand is zero. This non-function behavior is the result of the perfect competition assumption. Relax that assumption, and you get a smooth downward demand curve. Similarly, force production to require time, and interest rates a bit above or below the “best” rate no longer result in infinite or zero prices. They merely result in finite inflation or deflation.

  10. And I’d add that this is also why there was a need to introduce convex marginal adjustment costs — you need to introduce them only if production is instantaneous. If it is not instantaneous, then this serves as a type of natural break on infinite borrowing (leading to infinitely high prices), infinitely fast investment, or the production of infinite output in a single period.

    I’m going to post some mathematical examples in a later blog,

  11. Sergei says:

    “So we have to replace P(t+1) with people’s *expectations* of P(t+1)”

    Psychology says that people consistently and permanently over-expect. An interesting question then is what over-expectation means in terms of P(t+1).

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